Least squares method what is an good error

Question

Hi I have started using the least squares method and I want to calculate the mean error of my approximation. I use the following formular for calculating the error: $\ \mathcal E = ||A\hat x - y||/\sqrt n$ But how do I know if the error is big or low. Is it good to have a low number on $\ \mathcal E$ or should it be high?

Answer 1

$A\hat{x} - y = \hat{y} - y$ is the difference vector, and $\varepsilon$ is its norm divided by the constant $\sqrt{n}$. So $\varepsilon$ is a non-negative number. The smaller $\varepsilon$, the better the approximation.